Dr. J's Maths.com
Where the techniques of Maths
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Calculus - Integration - Reverse Chain Rule.
Test Yourself 1.


 

The questions on this page focus on:
1. Basic functions - indefinite integrals.
2. Basic functions - definite integrals.
3. More advanced questions.

They do not obtain solutions using logarithms.

You can access questions using the reverse chain rule involving logarithms elsewhere.

 

Use the Reverse Chain Rule approach involving substitution to integrate and/or evaluate the following :

Basic functions - indefinite. 1.

using the substitution u = x4 + 42.

 2.

using the substitution u = x3 + x2 - 8.
  3.

using the substitution u = x2 +x + 2.

 4.

using the substitution u = x2 - 1
  5. 6.
  7. . 8.

Hint.Use the substitution .
Basic functions - definite 9.

Answer.5216/3

 10. .

Hint.Use the substitution u = 2 + 2x - 2x2.

Answer.Integral = -8/3.
  11.
Answer.0.		 12.
Answer.10/21.
  13. Evaluate .
Hint.Use the substitution u = 2 + 2x - x2.

Answer.2(e4 - e2).

 14.
Answer.1.
  15. If and when x = √5, y = 2, find the equation for y in terms of x.

 
  16. Find the equation for x in terms of t if and
when t = 0, x = 10.

(Hint: use the substitution u = t2 - 2t + 4).